A345139 a(1) = 1; a(n) = a(n-1) + Sum_{d|n, d < n} a(d).

1, 2, 3, 6, 7, 13, 14, 23, 27, 37, 38, 63, 64, 81, 92, 124, 125, 171, 172, 225, 243, 284, 285, 396, 404, 471, 502, 606, 607, 762, 763, 919, 961, 1089, 1111, 1397, 1398, 1573, 1641, 1942, 1943, 2300, 2301, 2632, 2762, 3050, 3051, 3682, 3697, 4148, 4277, 4821, 4822, 5541, 5587

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

G.f. A(x) satisfies: A(x) = (1/(1 - x)) * (x + A(x^2) + A(x^3) + A(x^4) + ...).

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[If[d < n, a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]
nmax = 55; A[_] = 0; Do[A[x_] = (1/(1 - x)) (x + Sum[A[x^k], {k, 2, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A074206, A084978, A330575.

Sequence in context: A167415 A354361 A018511 * A182708 A304709 A330145

Adjacent sequences: A345136 A345137 A345138 * A345140 A345141 A345142

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 09 2021

Status

approved